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INVARIANT  TWINS
Sylvester almost ceased to be a mathematician. However, he
kept alive by taking a few private pupils, one of whom was to
leave a name that is known and revered in every country of the
world to-day. This was in the early 1850's, the 'potatoes,
prunes, and prisms' era of female propriety when young women
were not supposed to think of much beyond dabbling in paints
and piety. So it is rather surprising to find that Sylvester's most
distinguished pupil was a young woman, Florence Nightingale,
the first human being to get some decency and cleanliness into
military hospitals - over the outraged protests of bull-headed
military officialdom. Sylvester at the time was in his late
thirties, Miss Nightingale six years younger than her teacher.
Sylvester escaped from his makeshift ways of earning a living
in the same year (1854) that Miss Nightingale went out to the
Crimean War.
Before this, however, he had taken another false step that
landed him nowhere. In 1846, at the age of thirty-two, he
entered the Inner Temple (where he coyly refers to himself as
'a dove nestling among hawks5) to prepare for a legal career,
and in 1850 was called to the Bar. Thus he and Cayley came
together at last.
Cayley was twenty-nine, Sylvester thirty-six at the time;
both were out of the real jobs to which nature had called them.
Lecturing at Oxford thirty-five years later Sylvester paid
grateful tribute to 'Cayley, who, though younger than myself is
my spiritual progenitor - who first opened my eyes and purged
them of dross so that they could see and accept the higher
mysteries of our common Mathematical faith.1 In 1852, shortly
after their acquaintance began, Sylvester refers to 'Mr Cayley,
who habitually discourses pearls and rubies'. Mr Cayley for his
part frequently mentions Mr Sylvester, but always in cold
blood, as it were. Sylvester's earliest outburst of gratitude in
print occurs in a paper of 1851 where he says, 'The theorem
above enunciated [it is his relation between the minor deter-
minants of linearly equivalent quadratic forms] was in part
suggested in the course of a conversation with Mr Cayley (to
whom I am indebted for my restoration to the enjoyment of
mathematical life). .,.'
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